Shigley's mechanical engineering design (11th Ed.) 11th Edition Richard G. Budynas

Shigley's mechanical engineering design (11th Ed.) 11th Edition Richard G. Budynas
Shigley's mechanical engineering design (11th Ed.) 11th Edition Richard G. Budynas
Shigley's mechanical engineering design (11th Ed.) 11th Edition Richard G. Budynas

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7. Page iii

8. Shigley’s Mechanical
Engineering Design
Eleventh Edition
Richard G. Budynas
Professor Emeritus, Kate Gleason College of Engineering,
Rochester Institute of Technology
J. Keith Nisbett
Associate Professor of Mechanical Engineering,
Missouri University of Science and Technology

9. Page iv
SHIGLEY'S MECHANICAL ENGINEERING DESIGN, ELEVENTH EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2020 by McGraw-
Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2015, 2011,
and 2008. No part of this publication may be reproduced or distributed in any form or by any means, or
stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education,
including, but not limited to, in any network or other electronic storage or transmission, or broadcast for
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Some ancillaries, including electronic and print components, may not be available to customers outside the
United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 LWI 21 20 19
ISBN 978-0-07-339821-1 (bound edition)
MHID 0-07-339821-7 (bound edition)
ISBN 978-1-260-40764-8 (loose-leaf edition)
MHID 1-260-40764-0 (loose-leaf edition)
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Library of Congress Cataloging-in-Publication Data
Names: Budynas, Richard G. (Richard Gordon), author. | Nisbett, J. Keith,
author. | Shigley, Joseph Edward. Mechanical engineering design.
Title: Shigley's mechanical engineering design / Richard G. Budynas,
Professor Emeritus, Kate Gleason College of Engineering, Rochester
Institute of Technology, J. Keith Nisbett, Associate Professor of
Mechanical Engineering, Missouri University of Science and Technology.
Other titles: Mechanical engineering design

10. Description: Eleventh edition. ∣ New York, NY : McGraw-Hill Education, [2020]
∣ Includes index.
Identifiers: LCCN 2018023098 ∣ ISBN 9780073398211 (alk. paper) ∣ ISBN
0073398217 (alk. paper)
Subjects: LCSH: Machine design.
Classification: LCC TJ230 .S5 2020 | DDC 621.8/15--dc23 LC record available at
https://lccn.loc.gov/2018023098
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website
does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education
does not guarantee the accuracy of the information presented at these sites.

mheducation.com/highered

11. Page v






Dedication
To my wife, Joanne. I could not have accomplished what I have without your love and
support.
Richard G. Budynas
To my colleague and friend, Dr. Terry Lehnhoff, who encouraged me early in my
teaching career to pursue opportunities to improve the presentation of machine design
topics.
J. Keith Nisbett

12. Page vi

13. Dedication to Joseph Edward Shigley
Joseph Edward Shigley (1909–1994) is undoubtedly one of the most well-known and
respected contributors in machine design education. He authored or coauthored eight books,
including Theory of Machines and Mechanisms (with John J. Uicker, Jr.), and Applied
Mechanics of Materials. He was coeditor-in-chief of the well-known Standard Handbook of
Machine Design. He began Machine Design as sole author in 1956, and it evolved into
Mechanical Engineering Design, setting the model for such textbooks. He contributed to the
first five editions of this text, along with coauthors Larry Mitchell and Charles Mischke.
Uncounted numbers of students across the world got their first taste of machine design with
Shigley's textbook, which has literally become a classic. Nearly every mechanical engineer
for the past half century has referenced terminology, equations, or procedures as being from
“Shigley.” McGraw-Hill is honored to have worked with Professor Shigley for more than 40
years, and as a tribute to his lasting contribution to this textbook, its title officially reflects
what many have already come to call it—Shigley's Mechanical Engineering Design.
Having received a bachelor's degree in Electrical and Mechanical Engineering from
Purdue University and a master of science in Engineering Mechanics from the University of
Michigan, Professor Shigley pursued an academic career at Clemson College from 1936
through 1954. This led to his position as professor and head of Mechanical Design and
Drawing at Clemson College. He joined the faculty of the Department of Mechanical
Engineering of the University of Michigan in 1956, where he remained for 22 years until his
retirement in 1978.
Professor Shigley was granted the rank of Fellow of the American Society of Mechanical
Engineers in 1968. He received the ASME Mechanisms Committee Award in 1974, the
Worcester Reed Warner Medal for outstanding contribution to the permanent literature of
engineering in 1977, and the ASME Machine Design Award in 1985.
Joseph Edward Shigley indeed made a difference. His legacy shall continue.

14. Page vii

15. About the Authors
Richard G. Budynas is Professor Emeritus of the Kate Gleason College of Engineering at
Rochester Institute of Technology. He has more than 50 years experience in teaching and
practicing mechanical engineering design. He is the author of a McGraw-Hill textbook,
Advanced Strength and Applied Stress Analysis, Second Edition; and coauthor of a McGraw-
Hill reference book, Roark's Formulas for Stress and Strain, Eighth Edition. He was awarded
the BME of Union College, MSME of the University of Rochester, and the PhD of the
University of Massachusetts. He is a licensed Professional Engineer in the state of New York.
J. Keith Nisbett is an Associate Professor and Associate Chair of Mechanical Engineering at
the Missouri University of Science and Technology. He has more than 30 years of experience
with using and teaching from this classic textbook. As demonstrated by a steady stream of
teaching awards, including the Governor's Award for Teaching Excellence, he is devoted to
finding ways of communicating concepts to the students. He was awarded the BS, MS, and
PhD of the University of Texas at Arlington.

16. Page viii

17. 1
2
3
4
5
6
7
8
9
Brief Contents
Preface xv
Part 1
Basics 2
Introduction to Mechanical Engineering Design 3
Materials 41
Load and Stress Analysis 93
Deflection and Stiffness 173
Part 2
Failure Prevention 240
Failures Resulting from Static Loading 241
Fatigue Failure Resulting from Variable Loading 285
Part 3
Design of Mechanical Elements 372
Shafts and Shaft Components 373
Screws, Fasteners, and the Design of Nonpermanent Joints
421
Welding, Bonding, and the Design of Permanent Joints 485

18. 10
11
12
13
14
15
16
17
18
19
20
A
B
Page ix
Mechanical Springs 525
Rolling-Contact Bearings 575
Lubrication and Journal Bearings 623
Gears—General 681
Spur and Helical Gears 739
Bevel and Worm Gears 791
Clutches, Brakes, Couplings, and Flywheels 829
Flexible Mechanical Elements 881
Power Transmission Case Study 935
Part 4
Special Topics 954
Finite-Element Analysis 955
Geometric Dimensioning and Tolerancing 977
Appendixes
Useful Tables 1019
Answers to Selected Problems 1075
Index 1081

20. Page x

21. 1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
1-9
1-10
1-11
1-12
1-13
1-14
1-15
1-16
Contents
Preface xv
Part 1
Basics 2
Chapter 1
Introduction to Mechanical Engineering Design 3
Design 4
Mechanical Engineering Design 5
Phases and Interactions of the Design Process 5
Design Tools and Resources 8
The Design Engineer's Professional Responsibilities 10
Standards and Codes 12
Economics 13
Safety and Product Liability 15
Stress and Strength 16
Uncertainty 16
Design Factor and Factor of Safety 18
Reliability and Probability of Failure 20
Relating Design Factor to Reliability 24
Dimensions and Tolerances 27
Units 31
Calculations and Significant Figures 32

22. 1-17
1-18
2-1
2-2
2-3
2-4
2-5
2-6
2-7
2-8
2-9
2-10
2-11
2-12
2-13
2-14
2-15
2-16
2-17
2-18
2-19
2-20
2-21
2-22
Design Topic Interdependencies 33
Power Transmission Case Study Specifications 34
Problems 36
Chapter 2
Materials 41
Material Strength and Stiffness 42
The Statistical Significance of Material Properties 48
Plastic Deformation and Cold Work 50
Cyclic Stress-Strain Properties 57
Hardness 61
Impact Properties 62
Temperature Effects 63
Numbering Systems 64
Sand Casting 66
Shell Molding 66
Investment Casting 67
Powder-Metallurgy Process 67
Hot-Working Processes 67
Cold-Working Processes 68
The Heat Treatment of Steel 69
Alloy Steels 72
Corrosion-Resistant Steels 73
Casting Materials 73
Nonferrous Metals 75
Plastics 78
Composite Materials 80
Materials Selection 81

23. 3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
3-9
3-10
3-11
3-12
3-13
3-14
3-15
3-16
3-17
3-18
3-19
3-20
Page xi
Problems 87
Chapter 3
Load and Stress Analysis 93
Equilibrium and Free-Body Diagrams 94
Shear Force and Bending Moments in Beams 97
Singularity Functions 98
Stress 101
Cartesian Stress Components 101
Mohr's Circle for Plane Stress 102
General Three-Dimensional Stress 108
Elastic Strain 109
Uniformly Distributed Stresses 110
Normal Stresses for Beams in Bending 111
Shear Stresses for Beams in Bending 116
Torsion 123
Stress Concentration 132
Stresses in Pressurized Cylinders 135
Stresses in Rotating Rings 137
Press and Shrink Fits 139
Temperature Effects 140
Curved Beams in Bending 141
Contact Stresses 145
Summary 149
Problems 150
Chapter 4

24. 4-1
4-2
4-3
4-4
4-5
4-6
4-7
4-8
4-9
4-10
4-11
4-12
4-13
4-14
4-15
4-16
4-17
5-1
Deflection and Stiffness 173
Spring Rates 174
Tension, Compression, and Torsion 175
Deflection Due to Bending 176
Beam Deflection Methods 179
Beam Deflections by Superposition 180
Beam Deflections by Singularity Functions 182
Strain Energy 188
Castigliano's Theorem 190
Deflection of Curved Members 195
Statically Indeterminate Problems 201
Compression Members–General 207
Long Columns with Central Loading 207
Intermediate-Length Columns with Central Loading 210
Columns with Eccentric Loading 212
Struts or Short Compression Members 215
Elastic Stability 217
Shock and Impact 218
Problems 220
Part 2
Failure Prevention 240
Chapter 5
Failures Resulting from Static Loading 241
Static Strength 244

25. 5-2
5-3
5-4
5-5
5-6
5-7
5-8
5-9
5-10
5-11
5-12
5-13
6-1
6-2
6-3
6-4
6-5
6-6
6-7
6-8
6-9
6-10
Stress Concentration 245
Failure Theories 247
Maximum-Shear-Stress Theory for Ductile Materials 247
Distortion-Energy Theory for Ductile Materials 249
Coulomb-Mohr Theory for Ductile Materials 255
Failure of Ductile Materials Summary 258
Maximum-Normal-Stress Theory for Brittle Materials 262
Modifications of the Mohr Theory for Brittle Materials 263
Failure of Brittle Materials Summary 265
Selection of Failure Criteria 266
Introduction to Fracture Mechanics 266
Important Design Equations 275
Problems 276
Chapter 6
Fatigue Failure Resulting from Variable Loading
285
Introduction to Fatigue 286
Chapter Overview 287
Crack Nucleation and Propagation 288
Fatigue-Life Methods 294
The Linear-Elastic Fracture Mechanics Method 295
The Strain-Life Method 299
The Stress-Life Method and the S-N Diagram 302
The Idealized S-N Diagram for Steels 304
Endurance Limit Modifying Factors 309
Stress Concentration and Notch Sensitivity 320

26. 6-11
6-12
6-13
6-14
6-15
6-16
6-17
6-18
6-19
7-1
7-2
7-3
7-4
7-5
7-6
7-7
7-8
Page xii
Characterizing Fluctuating Stresses 325
The Fluctuating-Stress Diagram 327
Fatigue Failure Criteria 333
Constant-Life Curves 342
Fatigue Failure Criterion for Brittle Materials 345
Combinations of Loading Modes 347
Cumulative Fatigue Damage 351
Surface Fatigue Strength 356
Road Maps and Important Design Equations for the Stress-Life Method
359
Problems 363
Part 3
Design of Mechanical Elements 372
Chapter 7
Shafts and Shaft Components 373
Introduction 374
Shaft Materials 374
Shaft Layout 375
Shaft Design for Stress 380
Deflection Considerations 391
Critical Speeds for Shafts 395
Miscellaneous Shaft Components 400
Limits and Fits 406
Problems 411

27. 8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
8-9
8-10
8-11
8-12
9-1
9-2
9-3
9-4
9-5
Chapter 8
Screws, Fasteners, and the Design of
Nonpermanent Joints 421
Thread Standards and Definitions 422
The Mechanics of Power Screws 426
Threaded Fasteners 434
Joints–Fastener Stiffness 436
Joints–Member Stiffness 437
Bolt Strength 443
Tension Joints–The External Load 446
Relating Bolt Torque to Bolt Tension 448
Statically Loaded Tension Joint with Preload 452
Gasketed Joints 456
Fatigue Loading of Tension Joints 456
Bolted and Riveted Joints Loaded in Shear 463
Problems 471
Chapter 9
Welding, Bonding, and the Design of Permanent
Joints 485
Welding Symbols 486
Butt and Fillet Welds 488
Stresses in Welded Joints in Torsion 492
Stresses in Welded Joints in Bending 497
The Strength of Welded Joints 499

28. 9-6
9-7
9-8
9-9
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12
10-13
10-14
10-15
Static Loading 502
Fatigue Loading 505
Resistance Welding 507
Adhesive Bonding 508
Problems 516
Chapter 10
Mechanical Springs 525
Stresses in Helical Springs 526
The Curvature Effect 527
Deflection of Helical Springs 528
Compression Springs 528
Stability 529
Spring Materials 531
Helical Compression Spring Design for Static Service 535
Critical Frequency of Helical Springs 542
Fatigue Loading of Helical Compression Springs 543
Helical Compression Spring Design for Fatigue Loading 547
Extension Springs 550
Helical Coil Torsion Springs 557
Belleville Springs 564
Miscellaneous Springs 565
Summary 567
Problems 567
Chapter 11

29. 11-1
11-2
11-3
11-4
11-5
11-6
11-7
11-8
11-9
11-10
11-11
11-12
12-1
12-2
12-3
12-4
12-5
12-6
12-7
12-8
12-9
12-10
Page xiii
Rolling-Contact Bearings 575
Bearing Types 576
Bearing Life 579
Bearing Load Life at Rated Reliability 580
Reliability versus Life–The Weibull Distribution 582
Relating Load, Life, and Reliability 583
Combined Radial and Thrust Loading 585
Variable Loading 590
Selection of Ball and Cylindrical Roller Bearings 593
Selection of Tapered Roller Bearings 596
Design Assessment for Selected Rolling-Contact Bearings 604
Lubrication 608
Mounting and Enclosure 609
Problems 613
Chapter 12
Lubrication and Journal Bearings 623
Types of Lubrication 624
Viscosity 625
Petroff's Equation 627
Stable Lubrication 632
Thick-Film Lubrication 633
Hydrodynamic Theory 634
Design Variables 639
The Relations of the Variables 640
Steady-State Conditions in Self-Contained Bearings 649
Clearance 653

30. 12-11
12-12
12-13
12-14
12-15
13-1
13-2
13-3
13-4
13-5
13-6
13-7
13-8
13-9
13-10
13-11
13-12
13-13
13-14
13-15
13-16
13-17
Pressure-Fed Bearings 655
Loads and Materials 661
Bearing Types 662
Dynamically Loaded Journal Bearings 663
Boundary-Lubricated Bearings 670
Problems 677
Chapter 13
Gears–General 681
Types of Gears 682
Nomenclature 683
Conjugate Action 684
Involute Properties 685
Fundamentals 686
Contact Ratio 689
Interference 690
The Forming of Gear Teeth 693
Straight Bevel Gears 695
Parallel Helical Gears 696
Worm Gears 700
Tooth Systems 701
Gear Trains 703
Force Analysis–Spur Gearing 710
Force Analysis–Bevel Gearing 713
Force Analysis–Helical Gearing 716
Force Analysis–Worm Gearing 719
Problems 724

31. 14-1
14-2
14-3
14-4
14-5
14-6
14-7
14-8
14-9
14-10
14-11
14-12
14-13
14-14
14-15
14-16
14-17
14-18
14-19
Chapter 14
Spur and Helical Gears 739
The Lewis Bending Equation 740
Surface Durability 749
AGMA Stress Equations 751
AGMA Strength Equations 752
Geometry Factors I and J (Z
I and Y
J) 757
The Elastic Coefficient C
p (Z
E) 761
Dynamic Factor K
v 763
Overload Factor K
o 764
Surface Condition Factor C
f (Z
R) 764
Size Factor K
s 765
Load-Distribution Factor K
m (K
H) 765
Hardness-Ratio Factor C
H (Z
W) 767
Stress-Cycle Factors Y
N and Z
N 768
Reliability Factor K
R (Y
Z) 769
Temperature Factor K
T (Y
θ) 770
Rim-Thickness Factor K
B 770
Safety Factors S
F and S
H 771
Analysis 771
Design of a Gear Mesh 781
Problems 786
Chapter 15
Bevel and Worm Gears 791

32. 15-1
15-2
15-3
15-4
15-5
15-6
15-7
15-8
15-9
16-1
16-2
16-3
16-4
16-5
16-6
16-7
16-8
16-9
16-10
16-11
16-12
Page xiv
Bevel Gearing–General 792
Bevel-Gear Stresses and Strengths 794
AGMA Equation Factors 797
Straight-Bevel Gear Analysis 808
Design of a Straight-Bevel Gear Mesh 811
Worm Gearing–AGMA Equation 814
Worm-Gear Analysis 818
Designing a Worm-Gear Mesh 822
Buckingham Wear Load 825
Problems 826
Chapter 16
Clutches, Brakes, Couplings, and Flywheels 829
Static Analysis of Clutches and Brakes 831
Internal Expanding Rim Clutches and Brakes 836
External Contracting Rim Clutches and Brakes 844
Band-Type Clutches and Brakes 847
Frictional-Contact Axial Clutches 849
Disk Brakes 852
Cone Clutches and Brakes 856
Energy Considerations 858
Temperature Rise 860
Friction Materials 863
Miscellaneous Clutches and Couplings 866
Flywheels 868
Problems 873

33. 17-1
17-2
17-3
17-4
17-5
17-6
17-7
18-1
18-2
18-3
18-4
18-5
18-6
18-7
18-8
18-9
18-10
18-11
Chapter 17
Flexible Mechanical Elements 881
Belts 882
Flat- and Round-Belt Drives 885
V Belts 900
Timing Belts 908
Roller Chain 909
Wire Rope 917
Flexible Shafts 926
Problems 927
Chapter 18
Power Transmission Case Study 935
Design Sequence for Power Transmission 937
Power and Torque Requirements 938
Gear Specification 938
Shaft Layout 945
Force Analysis 947
Shaft Material Selection 947
Shaft Design for Stress 948
Shaft Design for Deflection 948
Bearing Selection 949
Key and Retaining Ring Selection 950
Final Analysis 953
Problems 953

34. 19-1
19-2
19-3
19-4
19-5
19-6
19-7
19-8
19-9
19-10
19-11
20-1
20-2
20-3
20-4
Part 4
Special Topics 954
Chapter 19
Finite-Element Analysis 955
The Finite-Element Method 957
Element Geometries 959
The Finite-Element Solution Process 961
Mesh Generation 964
Load Application 966
Boundary Conditions 967
Modeling Techniques 967
Thermal Stresses 970
Critical Buckling Load 972
Vibration Analysis 973
Summary 974
Problems 975
Chapter 20
Geometric Dimensioning and Tolerancing 977
Dimensioning and Tolerancing Systems 978
Definition of Geometric Dimensioning and Tolerancing 979
Datums 983
Controlling Geometric Tolerances 989

35. 20-5
20-6
20-7
20-8
20-9
A
B
Geometric Characteristic Definitions 992
Material Condition Modifiers 1002
Practical Implementation 1004
GD&T in CAD Models 1009
Glossary of GD&T Terms 1010
Problems 1012
Appendixes
Useful Tables 1019
Answers to Selected Problems 1075
Index 1081

36. Page xv

37. •
•
•
•
Preface
Objectives
This text is intended for students beginning the study of mechanical engineering design. The
focus is on blending fundamental development of concepts with practical specification of
components. Students of this text should find that it inherently directs them into familiarity
with both the basis for decisions and the standards of industrial components. For this reason,
as students transition to practicing engineers, they will find that this text is indispensable as a
reference text. The objectives of the text are to:
Cover the basics of machine design, including the design process, engineering mechanics
and materials, failure prevention under static and variable loading, and characteristics of
the principal types of mechanical elements.
Offer a practical approach to the subject through a wide range of real-world applications
and examples.
Encourage readers to link design and analysis.
Encourage readers to link fundamental concepts with practical component specification.

38. •
•
•
•
Page xvi
New to This Edition
Enhancements and modifications to the eleventh edition are described in the following
summaries:
Chapter 6, Fatigue Failure Resulting from Variable Loading, has received a complete
update of its presentation. The goals include clearer explanations of underlying
mechanics, streamlined approach to the stress-life method, and updates consistent with
recent research. The introductory material provides a greater appreciation of the
processes involved in crack nucleation and propagation. This allows the strain-life
method and the linear-elastic fracture mechanics method to be given proper context
within the coverage, as well as to add to the understanding of the factors driving the data
used in the stress-life method. The overall methodology of the stress-life approach
remains the same, though with expanded explanations and improvements in the
presentation.
Chapter 2, Materials, includes expanded coverage of plastic deformation, strain-
hardening, true stress and true strain, and cyclic stress-strain properties. This information
provides a stronger background for the expanded discussion in Chapter 6 of the
mechanism of crack nucleation and propagation.
Chapter 12, Lubrication and Journal Bearings, is improved and updated. The chapter
contains a new section on dynamically loaded journal bearings, including the mobility
method of solution for the journal dynamic orbit. This includes new examples and end-
of-chapter problems. The design of big-end connecting rod bearings, used in automotive
applications, is also introduced.
Approximately 100 new end-of-chapter problems are implemented. These are focused on
providing more variety in the fundamental problems for first-time exposure to the topics.
In conjunction with the web-based parameterized problems available through McGraw-
Hill Connect Engineering, the ability to assign new problems each semester is ever
stronger.
The following sections received minor but notable improvements in presentation:
Section 3-8 Elastic Strain
Section 3-11 Shear Stresses for Beams in Bending
Section 3-14 Stresses in Pressurized Cylinders

39. Section 3-15 Stresses in Rotating Rings
Section 4-12 Long Columns with Central Loading
Section 4-13 Intermediate-Length Columns with
Central Loading
Section 4-14 Columns with Eccentric Loading
Section 7-4 Shaft Design for Stress
Section 8-2 The Mechanics of Power Screws
Section 8-7 Tension Joints—The External Load
Section 13-5 Fundamentals
Section 16-4 Band-Type Clutches and Brakes
Section 16-8 Energy Considerations
Section 17-2 Flat- and Round-Belt Drives
Section 17-3 V Belts
In keeping with the well-recognized accuracy and consistency within this text, minor
improvements and corrections are made throughout with each new edition. Many of these are
in response to the diligent feedback from the community of users.

40. •
•
•
Instructor Supplements
Additional media offerings available at www.mhhe.com/shigley include:
Solutions manual. The instructor's manual contains solutions to most end-of-chapter
nondesign problems.
PowerPoint
®
slides. Slides outlining the content of the text are provided in PowerPoint
format for instructors to use as a starting point for developing lecture presentation
materials. The slides include all figures, tables, and equations from the text.
C.O.S.M.O.S. A complete online solutions manual organization system that allows
instructors to create custom homework, quizzes, and tests using end-of-chapter problems
from the text.

41. Acknowledgments
The authors would like to acknowledge those who have contributed to this text for over 50
years and eleven editions. We are especially grateful to those who provided input to this
eleventh edition:
Steve Boedo, Rochester Institute of Technology: Review and update of Chapter 12,
Lubrication and Journal Bearings.
Lokesh Dharani, Missouri University of Science and Technology: Review and advice
regarding the coverage of fracture mechanics and fatigue.
Reviewers of This and Past Editions
Kenneth Huebner, Arizona State
Gloria Starns, Iowa State
Tim Lee, McGill University
Robert Rizza, MSOE
Richard Patton, Mississippi State University
Stephen Boedo, Rochester Institute of Technology
Om Agrawal, Southern Illinois University
Arun Srinivasa, Texas A&M
Jason Carey, University of Alberta
Patrick Smolinski, University of Pittsburgh
Dennis Hong, Virginia Tech

42. Page xvii

43. List of Symbols
This is a list of common symbols used in machine design and in this book. Specialized use in
a subject-matter area often attracts fore and post subscripts and superscripts. To make the
table brief enough to be useful, the symbol kernels are listed. See Table 14–1 for spur and
helical gearing symbols, and Table 15–1 for bevel-gear symbols.
A Area, coefficient
a Distance
B Coefficient, bearing length
Bhn Brinell hardness
b Distance, fatigue strength exponent, Weibull shape parameter, width
C Basic load rating, bolted-joint constant, center distance, coefficient of variation,
column end condition, correction factor, specific heat capacity, spring index, radial
clearance
c Distance, fatigue ductility exponent, radial clearance
COVCoefficient of variation
D Diameter, helix diameter
d Diameter, distance
E Modulus of elasticity, energy, error
e Distance, eccentricity, efficiency, Naperian logarithmic base
F Force, fundamental dimension force
f Coefficient of friction, frequency, function
fom Figure of merit
G Torsional modulus of elasticity
g Acceleration due to gravity, function
H Heat, power
H
B Brinell hardness
HRCRockwell C-scale hardness
h Distance, film thickness
Combined overall coefficient of convection and radiation heat transfer
I Integral, linear impulse, mass moment of inertia, second moment of area
i Index
i Unit vector in x-direction
J Mechanical equivalent of heat, polar second moment of area, geometry factor
j Unit vector in the y-direction
K Service factor, stress-concentration factor, stress-augmentation factor, torque

44. Page xviii
coefficient
k Marin endurance limit modifying factor, spring rate
k Unit vector in the z-direction
L Length, life, fundamental dimension length
ℒ Life in hours
l Length
M Fundamental dimension mass, moment
M Moment vector, mobility vector
m Mass, slope, strain-strengthening exponent
N Normal force, number, rotational speed, number of cycles
n Load factor, rotational speed, factor of safety
n
d Design factor
P Force, pressure, diametral pitch
PDF Probability density function
p Pitch, pressure, probability
Q First moment of area, imaginary force, volume
q Distributed load, notch sensitivity
R Radius, reaction force, reliability, Rockwell hardness, stress ratio, reduction in area
R Vector reaction force
r Radius
r Distance vector
S Sommerfeld number, strength
s Distance, sample standard deviation, stress
T Temperature, tolerance, torque, fundamental dimension time
T Torque vector
t Distance, time, tolerance
U Strain energy
u Strain energy per unit volume
V Linear velocity, shear force
v Linear velocity
W Cold-work factor, load, weight
w Distance, gap, load intensity
X Coordinate, truncated number
x Coordinate, true value of a number, Weibull parameter
Y Coordinate
y Coordinate, deflection
Z Coordinate, section modulus, viscosity
z Coordinate, dimensionless transform variable for normal distributions
α Coefficient, coefficient of linear thermal expansion, end-condition for springs,
thread angle
β Bearing angle, coefficient
Δ Change, deflection

45. Page xix
δ Deviation, elongation
ϵ Eccentricity ratio
ε Engineering strain
ε˜ True or logarithmic strain
ε˜
f True fracture strain
ε′
f Fatigue ductility coefficient
Γ Gamma function, pitch angle
γ Pitch angle, shear strain, specific weight
λ Slenderness ratio for springs
μ Absolute viscosity, population mean
ν Poisson ratio
ω Angular velocity, circular frequency
ϕ Angle, wave length
ψ Slope integral
ρ Radius of curvature, mass density
σ Normal stress
σ
a Alternating stress, stress amplitude
σ
ar Completely reversed alternating stress
σ
m Mean stress
σ
0 Nominal stress, strength coefficient or strain-strengthening coefficient
σ′
f Fatigue strength coefficient
σ˜ True stress
σ˜
f True fracture strength
σ′ Von Mises stress
σˆ Standard deviation
τ Shear stress
θ Angle, Weibull characteristic parameter
¢ Cost per unit weight
$ Cost

46. Page xx

47. Page 2

48. part 1
Courtesy of Dee Dehokenanan

49. Chapter 1
Chapter 2
Chapter 3
Chapter 4
Basics
Introduction to Mechanical Engineering Design 3
Materials 41
Load and Stress Analysis 93
Deflection and Stiffness 173

50. Other documents randomly have
different content

51. The Undergraduate instruction in philosophy provides five hours a
week of required work for one year:
1) IN DEDUCTIVE AND INDUCTIVE LOGIC; 2) IN PSYCHOLOGY; 3) IN
ETHICS.
The courses are unified and thorough. A voluntary course in the
History of Philosophy is given; and advanced courses will be offered
this year in Modern Philosophy from Descartes to Kant, and in
English Ethics from Hobbes to Stephen. The instructors are
Professors Griffin and Emmot.

52. PERIODICALS.
MIND. July 1890. No. LIX.
CONTENTS:
OUR SPACE-CONSCIOUSNESS. A Reply. By Herbert Spencer.
VOLKMANN'S PSYCHOLOGY (I). By Thomas Whittaker.
THE LOGIC OF THE ETHIC OF EVOLUTION. By William Mitchell.
THE ANTINOMY OF THOUGHT. By Alexander F. Shand.
MENTAL TESTS AND MEASUREMENTS. By Prof. J. McK. Cattell.
    DISCUSSION: 1) The Evolution of Inductive Thought. By Hiram
M.
      Stanley.
      2) The Genesis of the Cognition of Physical Reality. By Julius
      Pikler.
    CRITICAL NOTICES: "Fouillée's L'Avenir de la Métaphysique
fondée

53.       sur l'Expérience"; Tarde's "Lois de l'Imitation"; Bæumker's
      "Das Problem der Materie in der Griechischen Philosophie."
SOME NEWLY-DISCOVERED LETTERS OF HOBBES. By the Editor.
Our Space-Consciousness. In this article Mr. Herbert Spencer
replies to criticisms, by adherents of Kantian doctrine, of objections
contained in §§ 326-335 of The Principles of Psychology. He objects
that the disciples of Kant "cannot imagine how it is possible that our
space-consciousness can have arisen out of that which was not
originally a space-consciousness."
Volkmann's Psychology. Shows that the really important point in
Volkmann's doctrine of "psychological mechanism" is its theory of
the interaction of contemporaneous presentations, and of the
existence among them of unconscious presentations. Herbartian
psychology is strictly scientific system, but when its superfluous
mechanism is cleared away, its explanations become those of
associationism.
In The Logic of the Ethic of Evolution, Mr. William Mitchell points
out that the two conditions of an ethical end are that it be the
motive of individual action, and that it furnish a critical system of
universal laws; and further that those conditions are fulfilled by the
end variously propounded in the ethic of evolution only if it be
represented, not as an external limit forcing itself on men, but as
presenting a more desirable character and medium to the individual
than any other. The end and means of moral progress given by the
Ethic of Evolution are perfectly true, but they do not express the
essence of the matter.

54. The Antinomy of Thought. This paper investigates an antinomy
which infects all our thought of reality that is not intuitive. The
source of error is the confusion of the judgment with the
consciousness or intuition of reality.
In the article on Mental Tests and Measurements, Prof. J. McK.
Cattell describes certain tests which are used in the Psychological
Laboratory of the University of Pennsylvania, with the object of
providing data for the discovery of the rules which govern the
constancy of mental processes, their interdependence, and their
variations under different circumstances.
The Evolution of Inductive Thought. A primary element in all
experience is its inductive quality. The struggle of existence awakens
experience to the thought-stage where it knows and directs itself,
but this very slowly. Development precedes self-development, and
this precedes a self-development which is self-conscious. This
conclusion is confirmed by some analyses of thought in the divisions
of conception, judgment, and reasoning.
The Genesis of the Cognition of Physical Reality. This is a criticism
by Mr. Julius Pikler of Mr. Stout's criticism on Mill, which appeared in
the January number of Mind. His opinion is that Mr. Strong's
statements are simply negations of Mill's theory, and as such prove
nothing.
Some newly-discovered Letters of Hobbes. These letters,
seventeen in number, were written to the French physician Sorbière,
and have been discovered by Dr. F. Tönnies in the National Library at
Paris. All of them, with related letters of Sorbière and others, are
given at length in the Archiv f. Gesch. d. Phil. iii. 58-71, 192-232,
and the first nine, which are the only ones of real importance, are

55. set out in this number of Mind. They have reference to the important
period of Hobbes's life and work that led up to Leviathan in 1651.
(London: Williams & Norgate.)
REVUE PHILOSOPHIQUE. No. 175. July 1890.
CONTENTS:
L'HOMOGENEITE MORALE. By G. Fonsegrive.
    CONTRIBUTIONS PSYCHO-PHYSIQUES A L'ETUDE
ESTHETIQUE (fin). By G.
      Sorel.
LA FOLIE DE J. J. ROUSSEAU. By H. Joly.
    LA PERCEPTION DES LONGUEURS ET DES NOMBRES CHEZ
QUELQUES PETITS
      ENF ANTS. By Alfred Binet.
ANALYSES ET COMPTES RENDUS.
M. Fonsegrive in L'Homogénéité morale points out the necessity of
a proper system of education for developing in the mind of the
young a moral homogeneity to replace the heterogeneity which
psychologists find in the nature of man.
In Contributions psycho-physiques a l'Etude esthétique, M. G.
Sorel continues his studies on the psychology of æsthetics, and
concludes that experimental psychology and especially psycho-
physics form the base of practical æsthetics.

56. M. H. Joly in La Folie de J. J. Rousseau points out that the problem
of the agreement of genius with insanity, so far as concerns
Rousseau, is reduced to small dimensions.
La Perception des Longueurs et des Nombres ches quelques petits
Enfants by M. Alfred Binet, describes certain original experiments
which indicate that young children have an accurate perception of
differences in length, but that their perception of number is very
limited. (Paris: F. Alcan.)
REVUE PHILOSOPHIQUE. No. 176. August 1890.
CONTENTS:
LES ORIGINES DE LA TECHNOLOGIE. By A. Espinas.
L'INHIBITION DANS LES PHÉNOMENES DE CONSCIENCE. By A.
Binet.
LA GÉOMÉTRIE GÉNÉRALE ET LES JUGEMENTS
SYNTHÉTIQUES A PRIORI. By G. Lechalas.
ANALYSES ET COMPTES RENDUS.
REVUE DES PERIODIQUES RUSSES.
CORRESPONDANCE: "Les Manuscrits de M. de Biran."
In Les Origines de la Technologie M. Espinas aims at giving a
history of philosophy in action. The present paper is devoted to
physico-theological technology, and concludes with the observation

57. that it was undoubtedly a progress to conceive the technical arts as
a whole, as a divine gift in like manner as the fruits of the earth and
the beneficent phenomena of nature, since this conception by
opposition gave rise to the idea of art, that is of human initiative
acting differently according to diversity of circumstances.
In L'Inhibition dans les Phénomènes de Conscience M. Alfred Binet
explains certain phenomena by showing that under various
circumstances certain images and sensations cannot coexist with
others in the same field of consciousness; the presence of one
excludes that of another. Antagonism and exclusion are the two
simple facts which explain the phenomena in question.
La Géométrie Générale et les Jugements Synthétiques a priori is a
reply by M. G. Lechalas to an article by M. Renouvier in the Critique
Philosophique criticising M. Calinon's theory of geometrical spaces
embodied in the system of "general geometry." While showing that
spaces with three dimensions are rationally included in a space with
four dimensions, M. Lechalas recognises the impossibility of
establishing such a geometry, seeing that we have no figure that
answers to what a four-dimensional space would be, as well as the
purely formal character of the presentations of non-Euclidian figures.
(Paris: F. Alcan.)
ZEITSCHRIFT FÜR PSYCHOLOGIE UND PHYSIOLOGIE DER
SINNESORGANE. Vol. I,
No. 2.
CONTENTS:

58.     UEBER DIE WAHRNEHMUNG UND LOKALISATION VON
SCHWEBUNGEN UND
      DIFFERENZTÖNEN. B y Carl L. Schaefer.
DIE ASSOCIATION SUCCESSIVER VORSTELLUNGEN. By H.
Münsterberg.
    BRIEFE VON G. TH. FECHNER: UEBER NEGATIVE
EMPFINDUNGSWERTE.
      (Concluded.) Edited by W. Preyer.
LITERATUR-BERICHT.
The results of Mr. Schaefer's researches are that for the
localisation of the vibrations of two tones, in the case of their
unequal relative intensity, the direction and distance of the relatively
louder tone are determinate. If the relative intensity of the primary
tones is equal, the vibrations are heard to proceed from the region
between the two sounding points. Differential tones are heard
between the ears, when the sounding sources are in the median
plane; but when both primary tones come from the same side, in or
immediately before the ear on that side; and in case of unequal
intensity, when both come from different sides, on the side of the
softer sound.
Prof. Münsterberg concludes that there is no successive
association of ideas; when successively appearing, they are received
singly into the memory.
The letters of Fechner are continued from No. 1.

59. ZEITSCHRIFT FÜR PSYCHOLOGIE UND PHYSIOLOGIE DER
SINNESORGANE. Vol. I,
No. 3.
CONTENTS:
    UEBER DIE KLEINSTEN WAHRNEHMBAREN GESICHTSWINKEL IN
DEN
      VERSCHIEDENEN TEILEN DES SPEKTRUMS . By W. Uhthoff.
DIE ÆSTHETISCHEN GEFUEHLE. By A. Döring.
    BESPRECHUNGEN: (1) A. Mosso's und A. Maggiora's "Ueber die
      Gesetze der Ermüdung." (2) Münsterberg's "Beitraege zur
      Experimentellen Psychologie."
LITERATUR-BERICHT.
Dr. Uhthoff, in order to determine the least visual angle of
perception, has employed a grating in a pure-monochromatic
spectral field. His results were that the angles in the different parts
of the spectrum are essentially equal.
Æsthetic emotions, Mr. Döring contends, proceed from the
unhindered play of the functions of psychical faculties; their contrary,
from the inhibition of the same.
This periodical is edited by H. Ebbinghaus and A. König, with H.
Aubert, S. Exner, H. v. Helmholtz, E. Hering, J. v. Kries, Th. Lipps, G.
E. Müller, W. Preyer, and C. Stumpf as collaborators. It appears every
two months. The review of the literature of its special department of
research is very comprehensive. (Hamburg and Leipsic: L. Voss.)

60. LA NUOVA FILOSOFIA.
RAGIONI E IDEALI. By La Direzione.
LA SENSAZIONE E LA SUA CONOSCIBILITA. By R. Ardigo.
    J. E. ALAUX'S LE PROBLEME RELIGIEUX AU XIX^e SIÈCLE. By
A.
      Torre.
ECONOMIA SCIENTIFICA ED ECONOMIA UTOPISTA. By A. Loria.
    P. LEROY-BEAULIEU'S L'ETAT MODERNE ET SES FONCTIONS.
By F. S.
      Nitti.
    C. JANNET'S LE SOCIALISME D'ETAT ET LA REFORME SOCIALE.
By F. S.
      Nitti.
    LOMBROSO'S AND LASCHI'S IL DELITTO POLITICO E LE
RIVOLUZIONI. By
      G. Fioretti.
CRITICA LETTERARIA.
    A. Angiulli—A. Saffi—F. Petruccelli della Gattina. (MEMORIE.)
      By A. Torre.
LA POLITICA.
QUESTIONI E PROBLEMI. La responsabilità filosofica,
secondo Paolo Janet.

61. This is the first number of La Nuova Filosofia which is established,
under the editorship of Dr. Andrea Torre, to diffuse in Europe and
America the best results of contemporary culture, in relation
especially to the life and development of society. (Naples: Dr. Andrea
Torre, Vico Lungo Avvocata, 66.)

62. APPENDIX.
Cut exhibiting modifications that affect the accessory nucleus.
Referred to on page 26 of this number of The Monist, in M. Binet's
article "The Immortality of Infusoria."
[Illustration: CONJUGATION OF CHILODON CUCULLULUS.]
A, beginning of conjugation; b, mouth; n, nucleus; nu, nucleolus;
v. c., multiple contracticle vesicles.
B, division of the nucleolus into two segments, nu', nu'; the
nucleus n begins to show signs of regression.
C, each of the two individuals in conjugation contains two
nucleolar segments, brought near together, of which one probably
comes from the individual opposite by course of exchange, and will
fuse with the segment not exchanged, to form a compound segment
(Maupas).
D, division of the segment into two portions which grow to
unequal sizes; the larger, nn, will become the new nucleus, the
smaller, the nucleolus of the new formation, nun.

63. E, the old nucleus, n, reduced to a small pale and rumpled mass,
is replaced by the new nucleus nn, near by which is seen the new
nucleolus nun.

64. VOL. I. JANUARY, 1891. NO. 2.

65. THE MONIST.

66. THE ARCHITECTURE OF THEORIES.
Of the fifty or hundred systems of philosophy that have been
advanced at different times of the world's history, perhaps the larger
number have been, not so much results of historical evolution, as
happy thoughts which have accidently occurred to their authors. An
idea which has been found interesting and fruitful has been adopted,
developed, and forced to yield explanations of all sorts of
phenomena. The English have been particularly given to this way of
philosophising; witness, Hobbes, Hartley, Berkeley, James Mill. Nor
has it been by any means useless labor; it shows us what the true
nature and value of the ideas developed are, and in that way affords
serviceable materials for philosophy. Just as if a man, being seized
with the conviction that paper was a good material to make things
of, were to go to work to build a papier mâché house, with roof of
roofing-paper, foundations of paste-board, windows of paraffined
paper, chimneys, bath tubs, locks, etc., all of different forms of
paper, his experiment would probably afford valuable lessons to
builders, while it would certainly make a detestable house, so those
one-idea'd philosophies are exceedingly interesting and instructive,
and yet are quite unsound.

67. The remaining systems of philosophy have been of the nature of
reforms, sometimes amounting to radical revolutions, suggested by
certain difficulties which have been found to beset systems
previously in vogue; and such ought certainly to be in large part the
motive of any new theory. This is like partially rebuilding a house.
The faults that have been committed are, first, that the dilapidations
have generally not been sufficiently thoroughgoing, and second, that
not sufficient pains has been taken to bring the additions into deep
harmony with the really sound parts of the old structure.
When a man is about to build a house, what a power of thinking
he has to do, before he can safely break ground! With what pains he
has to excogitate the precise wants that are to be supplied! What a
study to ascertain the most available and suitable materials, to
determine the mode of construction to which those materials are
best adapted, and to answer a hundred such questions! Now without
riding the metaphor too far, I think we may safely say that the
studies preliminary to the construction of a great theory should be at
least as deliberate and thorough as those that are preliminary to the
building of a dwelling-house.
That systems ought to be constructed architectonically has been
preached since Kant, but I do not think the full import of the maxim
has by any means been apprehended. What I would recommend is
that every person who wishes to form an opinion concerning
fundamental problems, should first of all make a complete survey of
human knowledge, should take note of all the valuable ideas in each
branch of science, should observe in just what respect each has
been successful and where it has failed, in order that in the light of
the thorough acquaintance so attained of the available materials for
a philosophical theory and of the nature and strength of each, he

68. may proceed to the study of what the problem of philosophy
consists in, and of the proper way of solving it. I must not be
understood as endeavoring to state fully all that these preparatory
studies should embrace; on the contrary, I purposely slur over many
points, in order to give emphasis to one special recommendation,
namely, to make a systematic study of the conceptions out of which
a philosophical theory may be built, in order to ascertain what place
each conception may fitly occupy in such a theory, and to what uses
it is adapted.
The adequate treatment of this single point would fill a volume,
but I shall endeavor to illustrate my meaning by glancing at several
sciences and indicating conceptions in them serviceable for
philosophy. As to the results to which long studies thus commenced
have led me, I shall just give a hint at their nature.
We may begin with dynamics,—field in our day of perhaps the
grandest conquest human science has ever made,—I mean the law
of the conservation of energy. But let us revert to the first step taken
by modern scientific thought,—and a great stride it was,—the
inauguration of dynamics by Galileo. A modern physicist on
examining Galileo's works is surprised to find how little experiment
had to do with the establishment of the foundations of mechanics.
His principal appeal is to common sense and il lume naturale. He
always assumes that the true theory will be found to be a simple
and natural one. And we can see why it should indeed be so in
dynamics. For instance, a body left to its own inertia, moves in a
straight line, and a straight line appears to us the simplest of curves.
In itself, no curve is simpler than another. A system of straight lines
has intersections precisely corresponding to those of a system of like
parabolas similarly placed, or to those of any one of an infinity of

69. systems of curves. But the straight line appears to us simple,
because, as Euclid says, it lies evenly between its extremities; that
is, because viewed endwise it appears as a point. That is, again,
because light moves in straight lines. Now, light moves in straight
lines because of the part which the straight line plays in the laws of
dynamics. Thus it is that our minds having been formed under the
influence of phenomena governed by the laws of mechanics, certain
conceptions entering into those laws become implanted in our
minds, so that we readily guess at what the laws are. Without such a
natural prompting, having to search blindfold for a law which would
suit the phenomena, our chance of finding it would be as one to
infinity. The further physical studies depart from phenomena which
have directly influenced the growth of the mind, the less we can
expect to find the laws which govern them "simple," that is,
composed of a few conceptions natural to our minds.
The researches of Galileo, followed up by Huygens and others, led
to those modern conceptions of Force and Law, which have
revolutionised the intellectual world. The great attention given to
mechanics in the seventeenth century soon so emphasised these
conceptions as to give rise to the Mechanical Philosophy, or doctrine
that all the phenomena of the physical universe are to be explained
upon mechanical principles. Newton's great discovery imparted a
new impetus to this tendency. The old notion that heat consists in an
agitation of corpuscles was now applied to the explanation of the
chief properties of gases. The first suggestion in this direction was
that the pressure of gases is explained by the battering of the
particles against the walls of the containing vessel, which explained
Boyle's law of the compressibility of air. Later, the expansion of
gases, Avogadro's chemical law, the diffusion and viscosity of gases,
and the action of Crookes's radiometer were shown to be

70. consequences of the same kinetical theory; but other phenomena,
such as the ratio of the specific heat at constant volume to that at
constant pressure require additional hypotheses, which we have little
reason to suppose are simple, so that we find ourselves quite afloat.
In like manner with regard to light, that it consists of vibrations was
almost proved by the phenomena of diffraction, while those of
polarisation showed the excursions of the particles to be
perpendicular to the line of propagation; but the phenomena of
dispersion, etc., require additional hypotheses which may be very
complicated. Thus, the further progress of molecular speculation
appears quite uncertain. If hypotheses are to be tried haphazard, or
simply because they will suit certain phenomena, it will occupy the
mathematical physicists of the world say half a century on the
average to bring each theory to the test, and since the number of
possible theories may go up into the trillions, only one of which can
be true, we have little prospect of making further solid additions to
the subject in our time. When we come to atoms, the presumption
in favor of a simple law seems very slender. There is room for
serious doubt whether the fundamental laws of mechanics hold good
for single atoms, and it seems quite likely that they are capable of
motion in more than three dimensions.
To find out much more about molecules and atoms, we must
search out a natural history of laws of nature, which may fulfil that
function which the presumption in favor of simple laws fulfilled in the
early days of dynamics, by showing us what kind of laws we have to
expect and by answering such questions as this: Can we with
reasonable prospect of not wasting time, try the supposition that
atoms attract one another inversely as the seventh power of their
distances, or can we not? To suppose universal laws of nature
capable of being apprehended by the mind and yet having no reason

71. for their special forms, but standing inexplicable and irrational, is
hardly a justifiable position. Uniformities are precisely the sort of
facts that need to be accounted for. That a pitched coin should
sometimes turn up heads and sometimes tails calls for no particular
explanation; but if it shows heads every time, we wish to know how
this result has been brought about. Law is par excellence the thing
that wants a reason.
Now the only possible way of accounting for the laws of nature
and for uniformity in general is to suppose them results of evolution.
This supposes them not to be absolute, not to be obeyed precisely.
It makes an element of indeterminacy, spontaneity, or absolute
chance in nature. Just as, when we attempt to verify any physical
law, we find our observations cannot be precisely satisfied by it, and
rightly attribute the discrepancy to errors of observation, so we must
suppose far more minute discrepancies to exist owing to the
imperfect cogency of the law itself, to a certain swerving of the facts
from any definite formula.
Mr. Herbert Spencer wishes to explain evolution upon mechanical
principles. This is illogical, for four reasons. First, because the
principle of evolution requires no extraneous cause; since the
tendency to growth can be supposed itself to have grown from an
infinitesimal germ accidentally started. Second, because law ought
more than anything else to be supposed a result of evolution. Third,
because exact law obviously never can produce heterogeneity out of
homogeneity; and arbitrary heterogeneity is the feature of the
universe the most manifest and characteristic. Fourth, because the
law of the conservation of energy is equivalent to the proposition
that all operations governed by mechanical laws are reversible; so
that an immediate corollary from it is that growth is not explicable

72. by those laws, even if they be not violated in the process of growth.
In short, Spencer is not a philosophical evolutionist, but only a half-
evolutionist,—or, if you will, only a semi-Spencerian. Now philosophy
requires thoroughgoing evolutionism or none.
The theory of Darwin was that evolution had been brought about
by the action of two factors: first, heredity, as a principle making
offspring nearly resemble their parents, while yet giving room for
"sporting," or accidental variations,—for very slight variations often,
for wider ones rarely; and, second, the destruction of breeds or
races that are unable to keep the birth rate up to the death rate.
This Darwinian principle is plainly capable of great generalisation.
Wherever there are large numbers of objects, having a tendency to
retain certain characters unaltered, this tendency, however, not
being absolute but giving room for chance variations, then, if the
amount of variation is absolutely limited in certain directions by the
destruction of everything which reaches those limits, there will be a
gradual tendency to change in directions of departure from them.
Thus, if a million players sit down to bet at an even game, since one
after another will get ruined, the average wealth of those who
remain will perpetually increase. Here is indubitably a genuine
formula of possible evolution, whether its operation accounts for
much or little in the development of animal and vegetable species.
The Lamarckian theory also supposes that the development of
species has taken place by a long series of insensible changes, but it
supposes that those changes have taken place during the lives of
the individuals, in consequence of effort and exercise, and that
reproduction plays no part in the process except in preserving these
modifications. Thus, the Lamarckian theory only explains the
development of characters for which individuals strive, while the

73. Darwinian theory only explains the production of characters really
beneficial to the race, though these may be fatal to individuals.[33]
But more broadly and philosophically conceived, Darwinian evolution
is evolution by the operation of chance, and the destruction of bad
results, while Lamarckian evolution is evolution by the effect of habit
and effort.
[33] The neo-Darwinian, Weismann, has shown that mortality
would almost necessarily result from the action of the Darwinian
principle.
A third theory of evolution is that of Mr. Clarence King. The
testimony of monuments and of rocks is that species are unmodified
or scarcely modified, under ordinary circumstances, but are rapidly
altered after cataclysms or rapid geological changes. Under novel
circumstances, we often see animals and plants sporting excessively
in reproduction, and sometimes even undergoing transformations
during individual life, phenomena no doubt due partly to the
enfeeblement of vitality from the breaking up of habitual modes of
life, partly to changed food, partly to direct specific influence of the
element in which the organism is immersed. If evolution has been
brought about in this way, not only have its single steps not been
insensible, as both Darwinians and Lamarckians suppose, but they
are furthermore neither haphazard on the one hand, nor yet
determined by an inward striving on the other, but on the contrary
are effects of the changed environment, and have a positive general
tendency to adapt the organism to that environment, since variation
will particularly affect organs at once enfeebled and stimulated. This
mode of evolution, by external forces and the breaking up of habits,
seems to be called for by some of the broadest and most important
facts of biology and paleontology; while it certainly has been the

74. chief factor in the historical evolution of institutions as in that of
ideas; and cannot possibly be refused a very prominent place in the
process of evolution of the universe in general.
Passing to psychology, we find the elementary phenomena of
mind fall into three categories. First, we have Feelings, comprising
all that is immediately present, such as pain, blue, cheerfulness, the
feeling that arises when we contemplate a consistent theory, etc. A
feeling is a state of mind having its own living quality, independent
of any other state of mind. Or, a feeling is an element of
consciousness which might conceivably override every other state
until it monopolised the mind, although such a rudimentary state
cannot actually be realised, and would not properly be
consciousness. Still, it is conceivable, or supposable, that the quality
of blue should usurp the whole mind, to the exclusion of the ideas of
shape, extension, contrast, commencement and cessation, and all
other ideas, whatsoever. A feeling is necessarily perfectly simple, in
itself, for if it had parts these would also be in the mind, whenever
the whole was present, and thus the whole could not monopolise the
mind.[34]
[34] A feeling may certainly be compound, but only in virtue of
a perception which is not that feeling nor any feeling at all.
Besides Feelings, we have Sensations of reaction; as when a
person blindfold suddenly runs against a post, when we make a
muscular effort, or when any feeling gives way to a new feeling.
Suppose I had nothing in my mind but a feeling of blue, which were
suddenly to give place to a feeling of red; then, at the instant of
transition there would be a shock, a sense of reaction, my blue life
being transmuted into red life. If I were further endowed with a

75. memory, that sense would continue for some time, and there would
also be a peculiar feeling or sentiment connected with it. This last
feeling might endure (conceivably I mean) after the memory of the
occurrence and the feelings of blue and red had passed away. But
the sensation of reaction cannot exist except in the actual presence
of the two feelings blue and red to which it relates. Wherever we
have two feelings and pay attention to a relation between them of
whatever kind, there is the sensation of which I am speaking. But
the sense of action and reaction has two types: it may either be a
perception of relation between two ideas, or it may be a sense of
action and reaction between feeling and something out of feeling.
And this sense of external reaction again has two forms; for it is
either a sense of something happening to us, by no act of ours, we
being passive in the matter, or it is a sense of resistance, that is, of
our expending feeling upon something without. The sense of
reaction is thus a sense of connection or comparison between
feelings, either, A, between one feeling and another, or B, between
feeling and its absence or lower degree; and under B we have, First,
the sense of the access of feeling, and Second, the sense of
remission of feeling.
Very different both from feelings and from reaction-sensations or
disturbances of feeling are general conceptions. When we think, we
are conscious that a connection between feelings is determined by a
general rule, we are aware of being governed by a habit. Intellectual
power is nothing but facility in taking habits and in following them in
cases essentially analogous to, but in non-essentials widely remote
from, the normal cases of connections of feelings under which those
habits were formed.

76. The one primary and fundamental law of mental action consists in
a tendency to generalisation. Feeling tends to spread; connections
between feelings awaken feelings; neighboring feelings become
assimilated; ideas are apt to reproduce themselves. These are so
many formulations of the one law of the growth of mind. When a
disturbance of feeling takes place, we have a consciousness of gain,
the gain of experience; and a new disturbance will be apt to
assimilate itself to the one that preceded it. Feelings, by being
excited, become more easily excited, especially in the ways in which
they have previously been excited. The consciousness of such a
habit constitutes a general conception.
The cloudiness of psychological notions may be corrected by
connecting them with physiological conceptions. Feeling may be
supposed to exist, wherever a nerve-cell is in an excited condition.
The disturbance of feeling, or sense of reaction, accompanies the
transmission of disturbance between nerve-cells or from a nerve-cell
to a muscle-cell or the external stimulation of a nerve-cell. General
conceptions arise upon the formation of habits in the nerve-matter,
which are molecular changes consequent upon its activity and
probably connected with its nutrition.
The law of habit exhibits a striking contrast to all physical laws in
the character of its commands. A physical law is absolute. What it
requires is an exact relation. Thus, a physical force introduces into a
motion a component motion to be combined with the rest by the
parallelogram of forces; but the component motion must actually
take place exactly as required by the law of force. On the other
hand, no exact conformity is required by the mental law. Nay, exact
conformity would be in downright conflict with the law; since it
would instantly crystallise thought and prevent all further formation

77. of habit. The law of mind only makes a given feeling more likely to
arise. It thus resembles the "non-conservative" forces of physics,
such as viscosity and the like, which are due to statistical
uniformities in the chance encounters of trillions of molecules.
The old dualistic notion of mind and matter, so prominent in
Cartesianism, as two radically different kinds of substance, will
hardly find defenders to-day. Rejecting this, we are driven to some
form of hylopathy, otherwise called monism. Then the question
arises whether physical laws on the one hand, and the psychical law
on the other are to be taken—
(A) as independent, a doctrine often called monism, but which I
would name neutralism; or,
(B) the psychical law as derived and special, the physical law
alone as primordial, which is materialism; or,
(C) the physical law as derived and special, the psychical law
alone as primordial, which is idealism.
The materialistic doctrine seems to me quite as repugnant to
scientific logic as to common sense; since it requires us to suppose
that a certain kind of mechanism will feel, which would be a
hypothesis absolutely irreducible to reason,—an ultimate,
inexplicable regularity; while the only possible justification of any
theory is that it should make things clear and reasonable.
Neutralism is sufficiently condemned by the logical maxim known
as Ockham's razor, i. e., that not more independent elements are to
be supposed than necessary. By placing the inward and outward
aspects of substance on a par, it seems to render both primordial.

78. The one intelligible theory of the universe is that of objective
idealism, that matter is effete mind, inveterate habits becoming
physical laws. But before this can be accepted it must show itself
capable of explaining the tridimensionality of space, the laws of
motion, and the general characteristics of the universe, with
mathematical clearness and precision; for no less should be
demanded of every Philosophy.
Modern mathematics is replete with ideas which may be applied to
philosophy. I can only notice one or two. The manner in which
mathematicians generalise is very instructive. Thus, painters are
accustomed to think of a picture as consisting geometrically of the
intersections of its plane by rays of light from the natural objects to
the eye. But geometers use a generalised perspective. For instance,
in the figure let O be the eye, let A B C D E be the edgewise view of
any plane, and let a f e D c be the edgewise view of another plane.
The geometers draw rays through O cutting both these planes, and
treat the points of intersection of each ray with one plane as
representing the point of intersection of the same ray with the other
plane. Thus, e represents E, in the painter's way. D represents itself.
C is represented by c, which is further from the eye; and A is
represented by a which is on the other side of the eye. Such
generalisation is not bound down to sensuous images. Further,
according to this mode of representation every point on one plane
represents a point on the other, and every point on the latter is
represented by a point on the former. But how about the point f
which is in a direction from O parallel to the represented plane, and
how about the point B which is in a direction parallel to the
representing plane? Some will say that these are exceptions; but
modern mathematics does not allow exceptions which can be
annulled by generalisation. As a point moves from C to D and thence

79. to E and off toward infinity, the corresponding point on the other
plane moves from c to D and thence to e and toward f. But this
second point can pass through f to a; and when it is there the first
point has arrived at A. We therefore say that the first point has
passed through infinity, and that every line joins in to itself
somewhat like an oval. Geometers talk of the parts of lines at an
infinite distance as points. This is a kind of generalisation very
efficient in mathematics.
[Illustration]
Modern views of measurement have a philosophical aspect. There
is an indefinite number of systems of measuring along a line; thus, a
perspective representation of a scale on one line may be taken to
measure another, although of course such measurements will not
agree with what we call the distances of points on the latter line. To
establish a system of measurement on a line we must assign a
distinct number to each point of it, and for this purpose we shall
plainly have to suppose the numbers carried out into an infinite
number of places of decimals. These numbers must be ranged along
the line in unbroken sequence. Further, in order that such a scale of
numbers should be of any use, it must be capable of being shifted
into new positions, each number continuing to be attached to a
single distinct point. Now it is found that if this is true for
"imaginary" as well as for real points (an expression which I cannot
stop to elucidate), any such shifting will necessarily leave two
numbers attached to the same points as before. So that when the
scale is moved over the line by any continuous series of shiftings of
one kind, there are two points which no numbers on the scale can
ever reach, except the numbers fixed there. This pair of points, thus
unattainable in measurement, is called the Absolute. These two

80. points may be distinct and real, or they may coincide, or they may
be both imaginary. As an example of a linear quantity with a double
absolute we may take probability, which ranges from an unattainable
absolute certainty against a proposition to an equally unattainable
absolute certainty for it. A line, according to ordinary notions, we
have seen is a linear quantity where the two points at infinity
coincide. A velocity is another example. A train going with infinite
velocity from Chicago to New York would be at all the points on the
line at the very same instant, and if the time of transit were reduced
to less than nothing it would be moving in the other direction. An
angle is a familiar example of a mode of magnitude with no real
immeasurable values. One of the questions philosophy has to
consider is whether the development of the universe is like the
increase of an angle, so that it proceeds forever without tending
toward anything unattained, which I take to be the Epicurean view,
or whether the universe sprang from a chaos in the infinitely distant
past to tend toward something different in the infinitely distant
future, or whether the universe sprang from nothing in the past to
go on indefinitely toward a point in the infinitely distant future,
which, were it attained, would be the mere nothing from which it set
out.
The doctrine of the absolute applied to space comes to this, at
either—
First, space is, as Euclid teaches, both unlimited and
immeasurable, so that the infinitely distant parts of any plane seen
in perspective appear as a straight line, in which case the sum of the
three angles of a triangle amounts to 180°; or,

81. Second, space is immeasurable but limited, so that the infinitely
distant parts of any plane seen in perspective appear as a circle,
beyond which all is blackness, and in this case the sum of the three
angles of a triangle is less than 180° by an amount proportional to
the area of the triangle; or,
Third, space is unlimited but finite, (like the surface of a sphere,)
so that it has no infinitely distant parts; but a finite journey along
any straight line would bring one back to his original position, and
looking off with an unobstructed view one would see the back of his
own head enormously magnified, in which case the sum of the three
angles of a triangle exceeds 180° by an amount proportional to the
area.
Which of these three hypotheses is true we know not. The largest
triangles we can measure are such as have the earth's orbit for
base, and the distance of a fixed star for altitude. The angular
magnitude resulting from subtracting the sum of the two angles at
the base of such a triangle from 180° is called the star's parallax.
The parallaxes of only about forty stars have been measured as yet.
Two of them come out negative, that of Arided (α Cygni), a star of
magnitude 1-1/2, which is -0."082, according to C. A. F. Peters, and
that of a star of magnitude 7-3/4, known as Piazzi III 422, which is
-0."045 according to R. S. Ball. But these negative parallaxes are
undoubtedly to be attributed to errors of observation; for the
probable error of such a determination is about ±0."075, and it
would be strange indeed if we were to be able to see, as it were,
more than half way round space, without being able to see stars
with larger negative parallaxes. Indeed, the very fact that of all the
parallaxes measured only two come out negative would be a strong
argument that the smallest parallaxes really amount to +0."1, were

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